Heath was climbing a mountain. 3 hours after he began climbing, he was at an altitude of 600 feet. After 5 hours, he is at an altitude of 900 feet.
Which equation shows the relationship between y, Heath’s altitude, and x, the number of hours he has been climbing?
The equation that shows the relationship between y, Heath's altitude, and x, the number of hours he has been climbing is:
y = 200x + 600
To find the equation that shows the relationship between Heath's altitude (y) and the number of hours he has been climbing (x), we can use the slope-intercept form of a linear equation which is y = mx + b.
We know that Heath's altitude increased by 300 feet over a period of 5 hours. To find the slope (m), we divide the change in altitude by the change in time:
m = (900 - 600) / (5 - 3) = 300 / 2 = 150
Next, we need to find the y-intercept (b). We can use one of the data points, for example, when he was at an altitude of 600 feet after 3 hours:
600 = 150(3) + b
600 = 450 + b
b = 600 - 450
b = 150
Finally, we have the slope (m) and the y-intercept (b), so the equation that represents the relationship between y (altitude) and x (time) is:
y = 150x + 150
To find the equation that represents the relationship between Heath's altitude (y) and the number of hours he has been climbing (x), we can use the concept of slope-intercept form: y = mx + b.
In this case, we know that after 3 hours, Heath was at an altitude of 600 feet, and after 5 hours, he was at an altitude of 900 feet.
First, let's find the slope (m):
The change in altitude (900 - 600) is 300 feet.
The change in time (5 - 3) is 2 hours.
So, the slope (m) is 300/2 = 150.
Now, we need to find the y-intercept (b), which represents Heath's altitude when x (number of climbing hours) is zero. We don't have this information directly, so we'll need to use the slope-intercept form and the given data points to solve for b.
Using the equation y = mx + b:
When x = 3 and y = 600:
600 = 150(3) + b
600 = 450 + b
b = 600 - 450
b = 150
Now that we have the values of m (150) and b (150), we can write the equation:
y = 150x + 150
So, the equation that shows the relationship between Heath's altitude (y) and the number of hours he has been climbing (x) is:
y = 150x + 150.